About the Perfect Number Checker
A perfect number equals the sum of its proper divisors, which are all the divisors except the number itself. The first is 6 = 1 + 2 + 3, and the next is 28 = 1 + 2 + 4 + 7 + 14. If the sum of the proper divisors is bigger than the number, it is abundant; if smaller, deficient. This checker adds up the divisors of any number up to a trillion and tells you which kind it is. Type a whole number and the perfect numbers appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Perfect Number Checker
- 1Enter a whole number.
- 2Pick the units or options from the menus if the perfect numbers tool offers them.
- 3Read the perfect numbers in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the perfect numbers
Number-theory lessons use perfect numbers to teach divisors. They have fascinated people since Euclid: every even perfect number comes from a Mersenne prime, and it is still not known whether an odd perfect number exists.
Only 52 perfect numbers are known, all even. The first four, 6, 28, 496 and 8,128, were known to the ancient Greeks. The fifth, 33,550,336, was found in the 15th century.
How the perfect numbers is worked out
Add all the divisors of n except n itself. Equal to n: perfect. Larger: abundant. Smaller: deficient. The divisors of 28 are 1, 2, 4, 7 and 14, which add to 28, so it is perfect. The number 12 has 1 + 2 + 3 + 4 + 6 = 16, so it is abundant. The number 13 is prime, with a divisor sum of 1, so it is deficient. The next perfect numbers are 496 and 8,128.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Shows divisors and sum
- Up to 10¹²
- Classifies abundant and deficient
Mistakes to avoid with perfect numbers
For large numbers the tool needs a moment, because it tries every possible divisor up to the square root. It accepts whole numbers from 1 up to 1,000,000,000,000. Numbers with more than 200 divisors show only the count and the sum, not the full list.
On phone and computer
On a phone, type into the boxes one after another and read the perfect numbers underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the perfect numbers move. The perfect number checker works the same on both. Perfect numbers are rare, and their factors are the key. Find those with the Factor Calculator, test for primes with the Prime Number Calculator, and look at other special numbers with the Armstrong Number Checker.
Features
- Proper divisors exclude n
- Even perfect numbers come from Mersenne primes
- Large inputs take a moment
- Clear messages when the perfect numbers inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate perfect numbers?
Add all the divisors of n except n itself. Equal to n: perfect. Larger: abundant. Smaller: deficient. The divisors of 28 are 1, 2, 4, 7 and 14, which add to 28, so it is perfect. The number 12 has 1 + 2 + 3 + 4 + 6 = 16, so it is abundant. The number 13 is prime, with a divisor sum of 1, so it is deficient. The next perfect numbers are 496 and 8,128.
What is the formula for perfect numbers?
Add all the divisors of n except n itself. Equal to n: perfect. Larger: abundant. Smaller: deficient. The perfect number checker applies it exactly and rounds only the displayed answer to six significant figures.
What are the first perfect numbers?
6, 28, 496, 8,128 and 33,550,336.
Is 1 perfect?
No. Its only proper divisor sum is 0, so it is deficient.
Are there odd perfect numbers?
None has been found, and none exists below 10 to the power of 1,500, but it is unproved that none exists.
Is this perfect number checker free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.